For a graph G and an integer-valued threshold function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the vertex set of G. We show that the problem of finding a dynamic monopoly of minimum order can be solved in polynomial time for interval graphs with bounded threshol...

We extend a result of Dubins (1975) from bounded to unbounded random variables. Dubins (1975) showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectations (conglom...

One basic goal in the analysis of time series data is to nd frequent interesting episodes i e collections of events occurring frequently together in the input sequence Most widely known work decide the interestingness of an episode from a xed user speci ed window width or interval that bounds the subsequent sequential association rules We present in this paper a more intuitive de nition that al...

This paper largely deals with some analytic properties of Brownian motion and those of its discrete counterpart, random walks. I prove that the random walker returns to the origin infinitely with probability one if and only if his coin is not biased. I then then show how to construct a continuous Brownian motion over the reals. While demonstrating this existence is in itself non-trivial, I show...

A family of orthogonal systems of irrational functions on the semi-infinite interval is introduced. The proposed orthogonal systems are based on Jacobi polynomials through an irrational coordinate transform. This family of orthogonal systems offers great flexibility to match a wide range of asymptotic behaviors at infinity. Approximation errors by the basic orthogonal projection and various oth...

We present a version of the Pontryagin Maximum Principle for control dynamics with a possibly non smooth, nonlipschitz and even discontinuous righthand side. The usual adjoint equation, where state derivatives occur, is replaced by an integrated form, containing only differentials of the reference flow maps. The resulting “integrated adjoint equation” leads to “adjoint vectors” that need not be...

We consider self-adjoint unbounded Jacobi matrices with diagonal qn = n and weights λn = cnn, where cn is a 2-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum is either purely absolutely continuous or discrete. This constitutes an example of the spectral phase transition of the first order. We study the lines where the spec...

This paper conducts a probabilistic analysis of an important class of heuristics for multiitem capacitated lot sizing problems. We characterize the asymptotic performance of so-called progressive interval heuristics as T , the length of the planning horizon, goes to infinity, assuming the data are realizations of a stochastic process of the following type: the vector of cost parameters follows ...

Given a word w over a 1nite alphabet and a set of ordered pairs of letters which de1ne adjacencies, we construct a graph which we call the letter graph of w. The lettericity of a graph G is the least size of the alphabet permitting to obtain G as a letter graph. The set of 2-letter graphs consists of threshold graphs, unbounded-interval graphs, and their complements. We determine the lettericit...